about slot math
January 12th, 2017 at 5:57:42 AM
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Hi all,
I am leaning some basic math for slot game. As an example, I use a very simple slot reels as follows by assuming 1 credit bet for each spin.
3xA, 30 HITS, awards 200 credits
2xA, 1000 HITS, awards 30 credits
3xK, 20 HITS, awards 500 credits
2xK, 200 HITS, awards 80 credits
3xQ, 10 HITS, awards 1000 credits
2xQ, 100 HITS, awards 200 credits
total CYCLE is 100,000 so there will be 98640 change out of 100,000 for no win. To calculate the return to player (RP), I get 0.92 so every 1 credit bet, I will get 0.92 credit back statistically. The 0.92 is also the average for my winning. The standard deviation (SD) of the game is 14.93. Here are two questions I have about those parameters
1) In some book about gaming math, I read the way to calculate SD is below
sqrt(sum (hit x (pay - RP)^2))/CYCLE)
here hit is the hit for each win AND that gives 0 pay. We calculate the SD in unit of credits, the return to player is no unit (or in percentage), how can we subtract a number from pay in credits? I guess here pay should be understood as pay per unit, so it does not have unit, right? If this is correct, does it mean if I pay 100 credits per spin, the pay in this formula should be actual pay divide by 100 in terms of calculating SD?
2) how do we understand the SD? As my understanding from statistics, SD tells how wide the range of probability could be to randomly pick something turns out to be around the average number. So if RP is 0.92, SD 14.93, can I say the return to player falls into 0.92-11.93 to 0.92+11.93 in the probability of over 68%? To me, it doesn't sound right since 0.92-11.93 is negative, what does it mean by that? Also, 11.93 is way larger than 0.92, should RP really have that much dispersion?
What I want to knows is as follows: let's say I play bunch of games. I divide my game play in N groups, each group if so 1,000,000 game plays. For each group, I get an RP close to 0.92 but not exact. So I will get N RP. What range will those RPs fall into? Does it has something to do with SD I compute above.
I am leaning some basic math for slot game. As an example, I use a very simple slot reels as follows by assuming 1 credit bet for each spin.
3xA, 30 HITS, awards 200 credits
2xA, 1000 HITS, awards 30 credits
3xK, 20 HITS, awards 500 credits
2xK, 200 HITS, awards 80 credits
3xQ, 10 HITS, awards 1000 credits
2xQ, 100 HITS, awards 200 credits
total CYCLE is 100,000 so there will be 98640 change out of 100,000 for no win. To calculate the return to player (RP), I get 0.92 so every 1 credit bet, I will get 0.92 credit back statistically. The 0.92 is also the average for my winning. The standard deviation (SD) of the game is 14.93. Here are two questions I have about those parameters
1) In some book about gaming math, I read the way to calculate SD is below
sqrt(sum (hit x (pay - RP)^2))/CYCLE)
here hit is the hit for each win AND that gives 0 pay. We calculate the SD in unit of credits, the return to player is no unit (or in percentage), how can we subtract a number from pay in credits? I guess here pay should be understood as pay per unit, so it does not have unit, right? If this is correct, does it mean if I pay 100 credits per spin, the pay in this formula should be actual pay divide by 100 in terms of calculating SD?
2) how do we understand the SD? As my understanding from statistics, SD tells how wide the range of probability could be to randomly pick something turns out to be around the average number. So if RP is 0.92, SD 14.93, can I say the return to player falls into 0.92-11.93 to 0.92+11.93 in the probability of over 68%? To me, it doesn't sound right since 0.92-11.93 is negative, what does it mean by that? Also, 11.93 is way larger than 0.92, should RP really have that much dispersion?
What I want to knows is as follows: let's say I play bunch of games. I divide my game play in N groups, each group if so 1,000,000 game plays. For each group, I get an RP close to 0.92 but not exact. So I will get N RP. What range will those RPs fall into? Does it has something to do with SD I compute above.
January 15th, 2017 at 4:40:12 AM
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For min rtp: Rtp - std deviation / sqrt number of spins
For max rtp: rtp + std deviation / sqrt number of spins
For max rtp: rtp + std deviation / sqrt number of spins
January 15th, 2017 at 9:19:08 AM
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Quote: Vip3r011For min rtp: Rtp - std deviation / sqrt number of spins
For max rtp: rtp + std deviation / sqrt number of spins
I use rtp +- 1.96*sd/sqrt(games). The sample should fall within this range 95% of the time.
I heart Crystal Math.
